Warp theory
A warp drive is a fictitious superluminal spacecraft propulsion system in many science fiction works, most notably Star Trek and I, Robot by Isaac Asimov. A spacecraft equipped with a warp drive may travel at speeds greater than that of light by many orders of magnitude. In contrast to some other fictitious FTL technologies such as a jump drive, the warp drive does not permit instantaneous travel between two points, but rather involves a measurable passage of time which is pertinent to the concept. In contrast to hyperdrive, spacecraft at warp velocity would continue to interact with objects in "normal space." The general concept of "warp drive" was introduced by John W. Campbell in his 1931 novel Islands of Space. Einstein's theory of special relativity states that energy and mass are interchangeable, and speed of light travel is impossible for material objects that weigh more than photons. The problem of a material object exceeding light speed is that an infinite amount of kinetic energy would be required to travel at exactly the speed of light. This can theoretically be solved by warping space to move an object instead of increasing the kinetic energy of the object to do so. Such a solution to the faster than light travel problem leads to two directly opposite approaches to light-speed travel in science fiction: in the first, spaceships themselves are brought to light speed and beyond; in the second, not-yet-local space itself is made to come to the ship while the ship moves at sub-light speeds. Contents Star Trek Original warp scale – The Original Series, The Animated Series, Enterprise, and Discovery Warp effect as depicted in Star Trek: The Original Series. Warp effect as depicted in Star Trek: The Next Generation. Warp drive is one of the fundamental features of the Star Trek franchise; in the first pilot episode of Star Trek: The Original Series, "The Cage", it is referred to as a "hyperdrive", with Captain Pike stating the speed to reach planet Talos IV as "time warp, factor 7". When beginning to explain travel times to the illusion survivors (before being interrupted by the sight of Vina), crewmember Jose stated that "the time barrier's been broken", allowing a group of interstellar travelers to return to Earth far sooner than would have otherwise been possible. Later in the pilot, when Spock is faced with the only action of escaping, he announces to the crew they have no choice but to leave, stating "Our time warp factor..." before the ship's systems start failing. In the second pilot for the original series, "Where No Man Has Gone Before", time was dropped from the speed setting with Kirk ordering speeds in simple "Ahead Warp Factor One", etc. that became so familiar from then on. The Warp drive velocity in Star Trek is generally expressed in "warp factor" units, which—according to Star Trek Star Fleet Technical Manual—corresponds to the magnitude of the warp field. Achieving warp factor 1 is equal to breaking the light barrier, while the actual velocity corresponding to higher factors is determined using an ambiguous formula. According to the Star Trek episode writer's guide for The Original Series, warp factors are converted to multiples of the speed of light by multiplication with the cubic function of the warp factor itself. Accordingly, "Warp 1" is equivalent to the speed of light, "Warp 2" is 8 times the speed of light, "Warp 3" is 27 times the speed of light, etc. Several episodes of the original series placed the Enterprise in peril by having it travel at high warp factors. However, the velocity (in present dimensional units) of any given warp factor is rarely the subject of explicit expression, and travel times for specific interstellar distances are not consistent through the various series. In the Star Trek: The Next Generation Technical Manual it was written that the real warp speed depends on external factors such as particle density or electromagnetic fields and only roughly corresponds with the calculated speed of current warp factor. The reference work Star Trek Maps established the theory of subspace (or warp) highways. In certain regions, a spaceship can fly at a multiple of the speed that corresponds to the current warp factor. In the original series, warp factor 6 was established as the common speed of the USS Enterprise NCC-1701. In some cases, the starship traveled at Warp 7 or above, but with risk of damaging the ship or the engines. Warp 9 in the original series was the "Never Exceed" speed for the hulls and engines of Constitution-class starships, equivalent to the aircraft VNE V-speed. Warp 6 was the VNO "Normal Operation" maximum safe cruising speed for that vessel class. Only five stories in the original Star Trek series involved the Enterprise traveling beyond Warp 9. In any instance, it was a result of the influence of alien beings or foreign technology. The Warp 14.1 incident in That Which Survives was the result of runaway engines which brought the hull within seconds of structural failure before power was disengaged.4 Later on, a prequel series titled Star Trek: Enterprise describes the warp engine technology as a "Gravimetric Field Displacement Manifold" (Commander Tucker's tour, "Cold Front"), and describes the device as being powered by a matter/anti-matter reaction which powers the two separate nacelles (one on each side of the ship) to create a displacement field. Enterprise, set in 2151 and onwards, follows the voyages of the first human ship capable of traveling at warp factor 5.2, which under the old warp table formula (the cube of the warp factor times the speed of light), is about 140 times the speed of light (i.e., 5.2 cubed). In the series pilot episode "Broken Bow", Capt. Archer equates Warp 4.5 to "Neptune and back Earth in six minutes" (which would correspond to a distance of 547 light-minutes or 66 au, consistent with Neptune being a minimum of 29 au distant from Earth). Modified warp scale – The Next Generation, Deep Space Nine and Voyager Michael Okuda's new warp scale For Star Trek: The Next Generation and the subsequent series, Star Trek artist Michael Okuda drew up a new warp scale and devised a formula based on the original one but with an important difference: In the half-open interval from 9 to 10, the exponent of w increases toward infinity. Thus, in the Okuda scale, warp velocities approach Warp 10 asymptotically. According to the Star Trek: The Next Generation Technical Manual there is no exact formula for this interval because the quoted velocities are based on a hand-drawn curve; what can be said is that at velocities greater than warp 9, the form of the warp function changes because of an increase in the exponent of the warp factor w. Due to the resultant increase in the derivative, even minor changes in the warp factor eventually correspond to a greater than exponential change in velocity. Warp Factor 10 was set as an unattainable maximum (according to the new scale, reaching or exceeding Warp 10 required an infinite amount of energy). This is described in Star Trek Technical Manuals as "Eugene's limit", in homage to creator/producer Gene Roddenberry. In Star Trek: The Next Generation Technical Manual it was established that the normal operating speed of the Enterprise-D (Galaxy class) was Warp 6 (new scale), the maximum rated cruise was Warp 9.2 and the maximum design speed of warp factor 9.6. In two episodes, the Enterprise-D could travel at warp 9.8 at "extreme risk", while fleeing from an enemy. According to the Star Trek: Deep Space Nine Technical Manual the Galaxy-class starships and some other starfleet vessels like Nebula class or Excelsior class were refitted during the Dominion War with newer technology including modifications which increased their maximum speed to Warp 9.9. According to the reference book USS Enterprise Owners' Workshop Manual the Enterprise-E can reach a maximum velocity of Warp 9.95. The Star Trek: Starship Spotter reference book states that the Intrepid-class starship Voyager has a maximum sustainable cruising speed of Warp 9.975, while the Prometheus-class can reach a maximum of Warp 9.99, with maximum cruising speed of Warp 9.9. As stated in the collection Star Trek Fact Files no ship, including highly developed ships like the Borg cube, may exceed warp factor 9.99 with her normal warp drive. To achieve higher speeds, the use of Transwarp technology is required. Warp velocities In the book Star Trek Encyclopedia, some warp velocities are given directly. For comparison, the following table shows these values and also the calculated speeds of the original warp scale, the calculated speeds of a simplified Okuda scale and some canonical reference values for warp speeds from onscreen sources. Warp factor Warp scale from Encyclopedia directly given values (Michael Okuda)5 Cubic warp scale v = w3c (Franz Joseph)6 Revised warp scale v = w10/3c (Michael Okuda)7 Onscreen Reference (Canon) (Multiple of speed of light) 1 1× 1× 1× 2 10× 8× 10× In the Star Trek: Enterprise episode "Dead Stop", it is said that Enterprise would take about a decade (10 years) to travel 130 light years at Warp 2. Thus Warp 2 corresponds to about 13 times the speed of light. 3 39× 27× 39× In the Star Trek: The Next Generation episode "The Most Toys" the crew of Enterprise-D discovers that the android Data may have been stolen while on board another ship, Jovis. At this point the Jovis, which has a maximum warp factor of 3, has had a 23-hour head start, which the Enterprise-D figures puts her anywhere within a 0.102 light year radius of her last known position. (By conversion, this implies that Warp 3 is equivalent to about 39c.) 4 102× 64× 102× In the Star Trek: Voyager episode "Resolutions", it is said that a Voyager shuttle would need about 700 years of flight time for a 70,000 light-year journey back to Earth. It follows that Warp 4, the stated maximum speed of the shuttle, is about 100 times the speed of light. 4.5 150× 91× 150× In the Star Trek: Enterprise pilot "Broken Bow", Commander Tucker states "warp 4.5 next Thursday", to which Captain Archer responds "Neptune and back in 6 minutes". The distance from Earth to Neptune varies all the time as both planets orbit the sun, however the average distance between the two is around 30.63 AU (4.58 billion km) and 29.76 AU (4.45 billion km) average 4.52 billion km. Therefore, a round trip of 9.04 billion km in 6 minutes would imply that Warp 4.5 is about 84 times the speed of light. 5 213× 125× 213× In the Star Trek: Enterprise episode "The Expanse", Captain Archer says the flight to the Delphice Expansion is equivalent to a 3-month trip. Upon arrival of the Enterprise, the distance to Earth is given as 50 light years. Thus, Warp 5, the maximum speed of the Enterprise, corresponds to about 200 times the speed of light. 6 392× 216× 392× 7 656× 343× 656× In the Star Trek: Enterprise episode "E²", the Enterprise will fly through an 11.6 light year long subspace corridor for a meeting with Degra. However, the Enterprise is thrown 127 years into the past. As the older Enterprise encounters their younger counterpart (to warn them), Captain Lorian suggests modifying the warp drive so that the younger Enterprise can briefly reach Warp Factor 6.9 and cover this distance in about two days without using the corridor. Thus, Warp 6.9 corresponds to about 2117 times the speed of light. In the Star Trek: Discovery episode "New Eden" (S2:E2), Commander Michael Burnham says a signal “is in the Beta Quadrant, 51,450 light years away,” to which Captain Christopher Pike replies, “at top speed that would take us 150 years to get that far,” indicating the maximum speed of Starship Discovery is 343x the speed of light (51,450 light years / 150 years). That responds to warp factor 7 of the original warp scale. 8 1024× 512× 1024× 9 1516× 729× 1516× In the episode Bloodlines from the series Star Trek: The Next Generation, Riker claims that the Enterprise would need around 20 minutes for a 300 billion kilometer flight at Warp 9. Thus Warp Factor 9 corresponds to a speed of 900 billion kilometers per hour (= 250 million kilometers per second) or about 830 times the speed of light. 9.9 3053× 970× 2083× In the episode The 37s from the Star Trek: Voyager series Warp 9.9 is directly mentioned in a dialog with 4 billion miles per second (6.5 billion km per second), which is about 21,468 times faster than the speed of light. 9.975 6395× 993× 2137× According to Gene Roddenberry's first concept script Star Trek is.., the original Enterprise had a maximum speed of 0.73 light years per hour, which is about 6395 times the speed of light. This corresponds roughly with Warp Factor 9.975 of the Okuda scale. 9.99 7912× 997× 2147× According to the episode Threshold from Star Trek: Voyager, Warp 9.99 is the beginning of Transwarp and the end of normal warp speeds. 9.9999 199,516× ~1000× ~2154× 10 Infinite velocity 1000× 2154× In the episode "Threshold", Tom Paris breaks the Warp 10 threshold, but travel beyond the threshold is later discovered to be unacceptably hazardous to biological life. In the episode "Where No One Has Gone Before" the Enterprise-D was shown to exceed warp 10, traveling 2.7 million light years from their home galaxy in a matter of minutes (though the ship's extreme velocity was due to the influence of an alien being and could not be achieved by starship engines). 11 Beyond scale 1331× 2960× In episode The Changeling the Enterprise briefly reached warp factor 11, as a result of Nomad's "correction of inefficiencies" in the antimatter control system. In the episode By Any Other Name the Kelvans modified the Enterprise's engines for greater sustained speed of warp factor 11 to travel from the Milky Way Galaxy to the Andromeda Galaxy. 12 1728× 3956× 13 2197× 5166× In the alternative future depicted in "All Good Things...", the series finale of The Next Generation, the "future" Enterprise-D travels at Warp 13, perhaps as a result of another reconfiguration of the warp scale. 14 2744× 6613× At one point in "That Which Survives" the Enterprise traveled at a warp factor of 14.1. 15 3375× 8323× 18.56 6395× – According to Gene Roddenberry's first concept script Star Trek is.., the original Enterprise had a maximum speed of 0.73 light years per hour, which is about 6395 times the speed of light. This corresponds with warp factor 18.56 of the cubic scale. Transwarp Transwarp generally refers to speeds and technologies that are beyond conventional warp drives. The warp drive has a natural physical or economical limit beyond which higher speeds are no longer possible. The reference work Star Trek Fact Files indicates this limit at warp factor 9.99. This is the highest conventional warp speed mentioned for a spaceship (Borg cube). Also in the episode Threshold (Star Trek Voyager) the warp factor 9.99 is suggested as the limit. This is the last warp factor mentioned before the leap takes place in the transwarp state. In the book Star Trek: The Next Generation Technical Manual the authors describes the idea of Transwarp: Finally, we had to create a back door for various powerful aliens like Q who got the knack of hurling the ship through the room for millions of light years during a commercial break. The Transwarp concept itself is not tied to any particular technology or speed limit. The first mention of a transwarp drive took place in the movie Star Trek III: The Search for Spock. There, the Starfleet developed a new spaceship type, the USS Excelsior (NX-2000), which should have a superior engine. The Excelsior captain plans to break the speed record of the USS Enterprise (Warp 14.1 cubic scale). The principle of this drive is not explained. Later, in Star Trek VI: The Undiscovered Country, the USS Excelsior had a normal warp drive. In Star Trek Fact Files it is stated that the experiment was a failure and the spaceship was converted to a normal warp drive. The entire episode Threshold from Star Trek Voyager is about a transwarp experiment by the USS Voyager crew. To get home faster, a shuttle is modified with novel dilithium crystals. The crew is trying to break the transwarp threshold. This threshold is between warp factor 9.99 and Warp 10 and transwarp itself represented the infinite speed. The shuttle allegedly found itself at all points in the universe at the same time during the flight. However, the pilot suffers genetic mutations after the flight, so it is not repeated. Due to the shuttle's limited memory, only a small portion of the sensor data was recorded. The entire experiment is described in the reference work Star Trek Fact Files. Some episodes later, fictionalized a few months later, the crew of USS Voyager encounters a species called the Voth. This species has spaceships with transwarp drive. However, this drive does not work on the basis of transwarp conduits, as the transwarp drive of the Borg, but is a further development of the conventional warp drive. The mention of a second Transwarp technology took place in the episode Descent of the series Star Trek: The Next Generation. A group of renegade Borg used transwarp conduits. These are wormhole-like tunnels through subspace. It was said in the dialogue that the flight through these tunnels was 20 times faster than the flight with maximum warp speed of the Enterprise. The flight itself was described as follows: "falling into a fast-moving river and getting swept away by the current." In the episode Endgame it is explained that the origin of these corridors was in six transwarp hubs spread across the galaxy. There were two ways to use these conduits outside these hubs. In TNG, the Enterprise was able to open such a channel with a precisely modulated tachyon impulse, traveling 65 light-years. However, when the USS Voyager tried the same thing in Day of Honor, the attempt failed and almost destroyed the ship. The second possibility is the use of the transwarp coil. In episode Dark Frontier the crew of Voyager steals such a coil from the Borg and is able to shorten their journey home by 15 years, before the coil burns out. Quantum Slipstream Another form of Transwarp used in Star Trek is called Quantum Slipstream. Similar to the Borg transwarp conduits, the slipstream is a narrowly focused, directed field that is initiated by manipulating the fabric of the space-time continuum using the starship's navigational deflector array. This creates a subspace tunnel, which is projected ahead of the vessel. Once a ship has entered this tunnel, the forces inside propel it at incredible speed. To maintain the slipstream, a ship has to constantly modify the quantum field with its deflector dish. The speed of the drive is inversely proportional to the time and distance. When the crew enters the Dauntless in the episode Hope and Fear for the first time and accidentally activates the propulsion system, the spaceship flies a flight of 15 light-years over a period of about 10 seconds. That is equivalent to approximately 50 million times the speed of light. After realizing that they would have to leave Voyager forever to get home with the Dauntless, the crew tries to match the drive of the USS Voyager to the parameters of the Dauntless. The modified Voyager is able to cover a distance of 300 light years with the slipstream modification before the system becomes unstable. The way back to Earth is stated in a fake message, created by Arturis, with 7 months aboard the Dauntless. For this period, the stocks are filled. At a residual distance of 60,000 light years at this time, this would correspond to a speed of about 100,000 times the speed of light or 1/500th of the time of a short slipstream jump. However, in the episode "Timeless", the technology proved to be dangerously unstable, resulting in the loss of all hands of the Voyager in an alternate timeline. Due to a phase variance, the slipstream tunnel, produced by a replica slipstream drive of the Voyager, collapsed during the flight and the ship crashed on a planet near the border on the edge of the Delta Quadrant. Harry Kim and Chakotay survived, because they used the Delta Flyer, which flew ahead of the Voyager, and reached the Earth safely. They used, some years after this event, a temporal communication device to change the timeline and rescue the ship and the crew. Folding space In addition to the possibility to let a spaceship glide through space in a warp field, there is also space folding in Star Trek. Spatial folding means that two points of space-time are directly connected and an instantaneous change takes place. The space between is simply folded into a higher-dimensional hyperspace or subspace. In the episode That Which Survives of the original series, the Enterprise encountered the remains of people called Kalandans. These are able to instantaneously teleport spaceships as well as people over long distances. In the episode Contagion of the series Star Trek: The Next Generation, the Enterprise-D discovered the former homeworld of the Iconians. These people were able to instantaneously teleport people over long distances with the help of Iconian Gateways. To ensure the gateway did not fall into the wrong hands, Captain Picard destroyed it. A year later, in The High Ground, terrorists on the planet Rutia IV used a space folding teleporter called an Inverter. However, this caused progressive physical harm to people during transport; multiple use almost always ended in death. The USS Voyager came in touch with this technology several times on their way home. In the episode Prime Factors the crew tried to buy a Spatial Trajector from the Sikarians. This wraps an object in a kind of subspace bubble, and teleports it to another location using spatial folding. The range was 40,000 light-years. However, the technology was not compatible with the warp core and almost destroyed Voyager when it was used. Three years later, in the episode Vis à Vis, Voyager discovered a stranded spaceship with a Coaxial Warp Drive. This also used spatial folding for locomotion. But the system was very unstable and if there is a fault in the drive it could cause a tear in the space-time continuum. A replica of the drive was only tested in a shuttle and never used for the Voyager. Last but not least, spatial folding appeared as a Geodesic Fold in the episode Inside Man. A geodesic fold occurs when a Verteron beam is fired at the atmosphere of a giant star at two different locations. This connects both points in space and creates a short lived passage. However, this was not usable because of deadly radiation that occurred during flight. A Ferengi ship's faked message from the Alpha Quadrant made the crew believe there was a safe passage. However, the Ferengi only wanted to get the Borg technology aboard Voyager and would have let the crew die. At the last moment, travel through the passage was aborted. Fictional history The episode "Metamorphosis", from The Original Series, establishes a backstory for the invention of warp drive on Earth, in which Zefram Cochrane discovered the "space warp". Cochrane is repeatedly referred to afterwards, but the exact details of the first warp trials were not shown until the second Star Trek: The Next Generation movie, Star Trek: First Contact. The movie depicts Cochrane as having first operated a warp drive on Earth in 2063. This successful first trial led directly to first contact with the Vulcans. It was also established that many other civilizations had warp drive before humans; First Contact co-writer Ronald D. Moore suggested Cochrane's drive was in some way superior to forms which existed beforehand, and was gradually adopted by the galaxy at large. Slingshot effect The "slingshot effect" is first depicted in "Tomorrow Is Yesterday" (1967) as a method of time travel. The procedure involves traveling at a high warp velocity in the proximity to a star, on a precisely calculated "slingshot" path; if successful, it causes a ship to enter a time warp, leading to the past or future. The same technique is used in the episode "Assignment: Earth" (1968) for historic research. The term "time warp" was first used in "The Naked Time" (1966) when a previously untried cold-start intermix of matter and antimatter threw the Enterprise back three days in time. The term was later used in Star Trek IV in describing the slingshot effect. The technique was mentioned as a viable method of time travel in the TNG episode "Time Squared" (1989). This "slingshot" effect has been explored in theoretical physics: it is hypothetically possible to slingshot oneself "around" the event horizon of a black hole. As a result of the black hole's extreme gravitation, time would pass at a slower rate near the event horizon, relative to the outside universe; the traveler would experience the passage of only several minutes or hours, while hundreds of years would pass in 'normal' space. Warp core A primary component of the warp drive method of propulsion in the Star Trek universe is the "gravimetric field displacement manifold", more commonly referred to as a warp core. It is a fictional reactor that taps the energy released in a matter-antimatter annihilation to provide the energy necessary to power a starship's warp drive, allowing faster-than-light travel. Starship warp cores generally also serve as powerplants for other primary ship systems. When matter and antimatter come into contact, they annihilate—both matter and antimatter are converted directly and entirely into enormous quantities of energy, in the form of subnuclear particles and electromagnetic radiation (specifically, mesons and gamma rays). In the Star Trek universe, fictional "dilithium crystals" are used to regulate this reaction. These crystals are described as being non-reactive to anti-matter when bombarded with high levels of radiation. Usually, the reactants are deuterium, which is an isotope of hydrogen, and antideuterium (its antimatter counterpart). In The Original Series and in-universe chronologically subsequent series, the warp core reaction chamber is often referred to as the "dilithium intermix chamber" or the "matter/antimatter reaction chamber", depending upon the ship's intermix type. The reaction chamber is surrounded by powerful magnetic fields to contain the anti-matter. If the containment fields ever fail, the subsequent interaction of the antimatter fuel with the container walls would result in a catastrophic release of energy, with the resultant explosion capable of utterly destroying the ship. Such "warp core breaches" are used as plot devices in many Star Trek episodes. An intentional warp core breach can also be deliberately created, as one of the methods by which a starship can be made to self-destruct. The mechanisms that provide a starship's propulsive force are the "warp nacelles", one (or more) cylindrical pods that are offset from the hull of the ship by large pylons; the nacelles generate the actual 'warp bubble' that surrounds the ship, and destruction of one or both nacelles will cripple the ship, and possibly cause a warp-core breach. Warp requirements for 10m OD sphere. Real-world theories and science In 1994, physicist Miguel Alcubierre formulated a theoretical solution, called the Alcubierre drive, for faster-than-light travel which models the warp drive concept. Calculations found that such a model would require prohibitive amounts of negative energy or mass. In 2018, the U.S. Defense Intelligence Agency made public a 2010 report that surveyed multiple different approaches to faster-than-light travel. One physicist who reviewed the report explained, that, while the theories were legitimate, they did not represent "something that's going to connect with engineering anytime soon, probably anytime ever." In 2012, NASA researcher Harold White hypothesized that by changing the shape of the warp drive, much less negative mass and energy could be used, though the energy required ranges from the mass of Voyager 1 to the mass of the observable universe, or many orders of magnitude greater than anything currently possible by modern technology. NASA engineers have begun preliminary research into such technology.